Why does the Pope not issue letters on the lines of Pastorals?
Perhaps it does happen from time to time. However, when the pope or the Holy See are involved it takes on a much greater degree of seriousness or urgency. Since such documents come from the pope and the Vatican it would certainly carry a different name. One such occasion was the Encyclical Letter of Pope Pius XI On the Church and the German Reich: Mit brennender Sorge.
Written in German, Pope Pius XI, it was smuggled into Germany for fear of censorship and was read from the pulpits of all German Catholic churches on one of the Church's busiest Sundays, Palm Sunday (21 March that year). Some pastors hid the encyclical inside the tabernacle, in order that the German authorities would not find it.
Mit brennender Sorge ("With burning concern") On the Church and the German Reich is an encyclical of Pope Pius XI, issued during the Nazi era on 10 March 1937 (but bearing a date of Passion Sunday, 14 March). Written in German, not the usual Latin, it was smuggled into Germany for fear of censorship and was read from the pulpits of all German Catholic churches on one of the Church's busiest Sundays, Palm Sunday (21 March that year).
The encyclical condemned breaches of the 1933 Reichskonkordat agreement signed between the German Reich and the Holy See. It condemned "pantheistic confusion", "neopaganism", "the so-called myth of race and blood", and the idolizing of the State. It contained a vigorous defense of the Old Testament with the belief that it prepares the way for the New. The encyclical states that race is a fundamental value of the human community, which is necessary and honorable but condemns the exaltation of race, or the people, or the state, above their standard value to an idolatrous level. The encyclical declares "that man as a person possesses rights he holds from God, and which any collectivity must protect against denial, suppression or neglect." National Socialism, Adolf Hitler and the Nazi Party are not named in the document. The term for the German government (Reichsregierung) is used.
The effort to produce and distribute over 300,000 copies of the letter was entirely secret, allowing priests across Germany to read the letter without interference. The Gestapo raided the churches the next day to confiscate all the copies they could find, and the presses that had printed the letter were closed. According to historian Ian Kershaw, an intensification of the general anti-church struggle began around April in response to the encyclical. Scholder wrote: "state officials and the Party reacted with anger and disapproval. Nevertheless the great reprisal that was feared did not come. The concordat remained in force and despite everything the intensification of the battle against the two churches which then began remained within ordinary limits." The regime further constrained the actions of the Church and harassed monks with staged prosecutions. Though Hitler is not named in the encyclical, it does refer to a "mad prophet" that some claim refers to Hitler himself.
The actual encyclical can be read here.
More closer to our own day and age, Pope John Paul II called the Great, wrote a number of pastoral letters. For example, his Letters to Priests were published every Holy Thursday for all priests throughout the world.
Pastoral letters (Wikipedia)
Letter to Children, 1994
Letter to Families (Gratissima Sane), 1994
Letter to Priests, 1994
Letter to the Secretary General of the International Conference on Population and Development, 1994
Letter to Women, 1995.
Link to other letters on the Vatican website.